ALEXANDER JONES CALENDRICA I: NEW CALLIPPIC DATES aus: Zeitschrift für Papyrologie und Epigraphik 129 (2000) 141–158 © Dr. Rudolf Habelt GmbH, Bonn 141 CALENDRICA I: NEW CALLIPPIC DATES 1. Introduction. Callippic dates are familiar to students of Greek chronology, even though up to the present they have been known to occur only in a single source, Ptolemy’s Almagest (c. A.D. 150).1 Ptolemy’s Callippic dates appear in the context of discussions of astronomical observations ranging from the early third century B.C. to the third quarter of the second century B.C. In the present article I will present new attestations of Callippic dates which extend the period of the known use of this system by almost two centuries, into the middle of the first century A.D. I also take the opportunity to attempt a fresh examination of what we can deduce about the Callippic calendar and its history, a topic that has lately been the subject of quite divergent treatments. The distinguishing mark of a Callippic date is the specification of the year by a numbered “period according to Callippus” and a year number within that period. Each Callippic period comprised 76 years, and year 1 of Callippic Period 1 began about midsummer of 330 B.C. It is an obvious, and very reasonable, supposition that this convention for counting years was instituted by Callippus, the fourth- century astronomer whose revisions of Eudoxus’ planetary theory are mentioned by Aristotle in Metaphysics Λ 1073b32–38, and who also is prominent among the authorities cited in astronomical weather calendars (parapegmata).2 The point of the cycles is that 76 years contain exactly four so-called Metonic cycles of 19 years. The Metonic cycle reflects the fact that 235 lunar months, reckoned (for example) from full moon to full moon or from new moon crescent to new moon crescent, are practically indistinguishable in length from 19 solar years, reckoned from solstice to the same kind of solstice, or equinox to the same kind of equinox. This relation provides a convenient basis for regulating a lunar calendar so that the beginning of the year will not drift outside a particular season. It is merely necessary to establish a repeating cycle of nineteen calendar years, twelve containing twelve lunar months, and seven containing thirteen months. A convention for naming the months is also needed, one method being to have twelve names in a fixed order, and to stipulate that in the thirteen-month years a particular month will occur twice in a row. The doubled month need not be the same in all thirteen-month years, but it should be the same for all years that have the same position in the nineteen-year cycles. By distributing the thirteen-month years evenly in the nineteen-year cycle one can keep the beginning of the lunar year as close as possible to a particular point in the solar year. Years can be named in any traditional way, for example according to magistrates or regnal years. The beginnings of the lunar months can be determined by observation, for example by the sighting of the new moon crescent. If this is the practice, then the Metonic cycle only regulates the beginnings of years and the naming of months. Alternatively, one can set out a fixed pattern of thirty-day (“full”) months and twenty-nine-day (“hollow”) months covering the entire 235-month cycle. A Metonic cycle of this kind additionally regulates the beginnings of months and the naming of days. For it to work well, 1 The literature on the Callippic periods is extensive. Because for the sake of clarity I have eschewed a historiographical manner of presentation in this article, I should acknowledge that there is little in sections 1 and 2 that someone has not said before. Older discussions and reconstructions are reviewed in sufficient detail by Ginzel, HMTC v. 1, 409–419. Fothering- ham (1924) is fundamental to more recent work; see also Samuel (1972) and van der Waerden (1960) and (1984). The interesting, complicated historical reconstruction of Goldstein & Bowen (1989) is based on a false premise, as I have shown in Jones (1997) 157–158 and 166 n. 25. 2 See the parapegmata of pseudo-Geminus (Geminus ed. Manitius, 210–232) and Ptolemy (Opera astronomica minora, ed. Heiberg, 3–67) passim. Callippus is specifically credited with the principle of a 76-year calendrical cycle by Geminus (ed. Manitius, 120–122), who does not however mention the Callippic periods as such. Goldstein & Bowen (1989) elaborate a theory that the Callippic periods were instituted only late in the third century B.C. 142 A. Jones one has to have the total number of days in the cycle correspond as nearly as possible to the number of days in an observed interval of 235 lunar months, or alternatively in an observed interval of nineteen solar years. Moreover the distribution of full and hollow months should be, broadly speaking, uniform through the cycle. There is, however, no need to count the number of days in an actual Metonic cycle; it will suffice to have an estimate of the length of the average month or of the year. Taking the approximation 1 year = 365 1/4 days (1) we obtain the relationship: 235 months = 19 years = 6939 3/4 days (2) To have a cycle comprising a whole number of days, we have to multiply these numbers by four: 940 months = 76 years = 27759 days (3) This is the derivation of the Callippic periods. It stands to reason that a practice of naming years according to their position in 76-year periods ought to go along with a lunar calendar in which the sequence of months is regulated by a Metonic cycle repeated four times, and the distribution of full and hollow months is determined so as to satisfy relation (3). Without regulation of the lengths of the months and hence the total number of days in a cycle, the 76-year period would have no advantage over the 19-year period. 2. The oldest Callippic dates. In the following we shall use the abbreviation CP1 for “first period according to Callippus,” and so forth. The Callippic dates in Ptolemy’s Almagest belong to CP1 (year 1 = 330/329 B.C.), CP2 (year 1 = 254/253 B.C.), and CP3 (year 1 = 178/177 B.C.). All are dates of astronomical observations. The earliest four, a set of observations of the moon by a certain Timocharis,3 are as follows (Alm. VII 3, ed. Heiberg v. 2, 25–32): [1] Again, Timocharis, who observed at Alexandria, says that in year 36 of the first period according to Callippus, on Poseideon 25, which is Phaophi 16, when the tenth hour was beginning, the moon was seen with great accuracy as having overtaken with its northern rim the northern one of the stars on the forehead of Scorpius. [According to Ptolemy, this was Era Nabonassar 454, Phaophi 16/17, i.e. 295 B.C. December 20/21; the date is confirmed by the astronomical content.] [2] Again, Timocharis, who observed at Alexandria, records that in year 36 of the first period according to Callippus, on Elaphebolion 15, which is Tybi 5, as the third hour was beginning, the moon overtook Spica with the middle of the part of its rim that points towards the equinoctial rising, and Spica traversed it, cutting off exactly one third of its diameter on the north side. [According to Ptolemy, this was Era Nabonassar 454, Tybi 5/6, i.e. 294 B.C. March 9/10; the date is confirmed by the astronomical content.] [3] Timocharis, who observed these things at Alexandria, records that in year 47 of the first 76- year period according to Callippus, on Anthesterion 8, which is Hathyr 29 according to the Egyptians, as the third hour was ending, the southern half part of the moon was seen to cover exactly either the trailing third or the trailing half of the Pleiades. [According to Ptolemy, this was Era Nabonassar 465 Hathyr 29/30, i.e. 283 B.C. January 29/30; the date is confirmed by the astronomical content.] 3 The Almagest also preserves a report of two observations of Venus in 272 B.C. by Timocharis (X 4, ed. Heiberg v. 2, 310–311), lacking any trace of Callippic dating, as well as undated measurements of stellar declinations (VII 3, ed. Heiberg v. 2, 19–23). A scholion to Aratus (Scholia in Aratum Vetera ed. Martin, 213) suggests that Timocharis wrote a description of the constellations or catalogue of stars. His name appears in broken context at the end of an arithmetical scheme for predicting Venus’ motion in longitude, P. Oxy. LXI.4135 in Jones (1999). Calendrica I: New Callippic Dates 143 [4] Likewise, in year 48 of the same [i.e. the first] period, he says that on Pyanepsion 6 waning [tª wÄ fy¤nontow, i.e. the 25th], which is Thoth 7, when as much as half an hour of the tenth hour had passed and the moon was risen above the horizon, Spica was seen to touch the very northern part exactly. [According to Ptolemy, this was Era Nabonassar 466, Thoth 7/8, i.e. 283 B.C. November 8/9; the date is confirmed by the astronomical content.] Ptolemy gives the date of each observation twice: once at the beginning of the report, and a second time in his ensuing analysis. The second version gives the date according to Ptolemy’s own preferred convention, using Egyptian calendar months and days, with years counted serially from the first (Egyptian!) regnal year of the Babylonian king Nabonassar (reigned 747–734 B.C.).4 Since the observations are all nocturnal, Ptolemy avoids ambiguity by giving the day numbers of both the preceding and following days.